I've always thought that it was because he kept a record book of the betting transactions, but I can find no confirmation or refutation online.
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Mister Micawberhe kept a record book of the betting transactionsbookmaker (n.) (later, shortened to "bookie") also book-maker, 1510s, "printer and binder of books," from book (n.) + agent noun from make (v.). The wagering sense is from 1862. Related: Book-making (late 15c., betting sense 1824).